The Linear Optical Amplifier (LOA) is a chip-based amplifier that addresses many of the requirements of emerging optical networks: operation under diverse bit rates, channel counts, and switching protocols, as well as reduced cost and size. In this work, we discuss, in detail, the design and operation of the LOA. Specifically, we consider the performance characteristics of the VCSEL and the amplifier, as well as the relationship between the two. Resulting trade-offs are also discussed.
The Linear Optical Amplifier (LOA) is a chip-based amplifier that addresses many of the requirements of emerging optical networks: operation under diverse bit rates, channel counts, and switching protocols, as well as reduced cost and size. In this work, we review the operating principles of the LOA, and describe two versions of the LOA technology. The first is a polarization-independent amplifier that operates over the entire C-band. We present several examples of this technology's system performance, and also highlight its value in coarse wavelength-division multiplexing (CWDM) applications. We also demonstrate a new, single polarization LOA technology, which is designed to deliver high linear gain over an extended range of output powers. We measure typical chip gains in excess of 20dB, and demonstrate linear gain performance for an (average) chip power approaching 15dBm. These results indicate that this technology is well-suited for long-reach, 10Gbps transmitter boost applications.
We analyze the effect of plasma density fluctuations on x-ray laser coherence and discuss the implications of our results for exploding-foil x-ray laser experiments. We treat propagation of coherence using a deterministic ray-tracing technique based on the radiation transfer equation, coupled with the phase approximation of Huygens-Kirchhoff method to treat the random fluctuations. First we develop the propagation technique for the zero-fluctuation case, and derive analytical solutions for the intensity distribution and coherence function in the output plane of an active medium with parabolic transverse profiles of dielectric constant and gain coefficient. We discuss under what conditions we may include only the contribution of spontaneous sources adjacent to the far face of the active medium, and show that in many practical cases it is necessary to take into account sources throughout the whole active medium. We then include density fluctuations, and obtain expressions for the coherence function for homogeneous fluctuations with both Gaussian and exponential correlation, as a function of fluctuation amplitude and correlation length. We apply our results to selenium and yttrium exploding foil x-ray lasers, where non- uniformity in the optical laser pump beams or hydrodynamic instabilities may lead to fluctuations. We show how fluctuations can cause the coherence to saturate with increasing laser length, and indicate how a moderate level of fluctuations can explain the observed coherence in experiments on selenium x-ray lasers. We also characterize the sensitivity of the coherence to fluctuations by defining critical amplitude level above which they dominate the coherence.
To implement optical submodules or systems of the future we have identified a few key components and technologies necessary to build optical products at Hewlett Packard. To be competitive these optical assemblies must be smaller, cheaper and more functional, then current optical products while maintaining or exceeding the existing performance level. To accomplish this task we introduce the idea of a silicon micro- optical bench (SMOB). The focus of the micro-optical bench has been laser submounts and collimators. However, while making advances in these platform technologies, the importance of micro parts which can be used to augment and expand the optical functions has become apparent. In this paper the role of silicon as a micro-optical bench substrate is described along with implementations of micro-optical benches. Silicon is an excellent choice as a base platform for SMOB technology because of its availability and excellent material properties and advanced processing technology. Structures to aid in batch assembly processes are easily constructed from silicon wafers. We show how to create structures which allow placement of ball lenses and other three dimensional structures to 1 micrometer accuracy. This can be accomplished in a batch process with the potential for reductions in cost of assembly. We have built generic laser submounts and collimators with various sizes of ball lenses. We show how the performance of these submounts agrees with the theoretical predictions. For fiber to ball coupling Gaussian methods work well. However, for laser to fiber coupling via ball lenses it is necessary to use a Maxwell equation solver in spherical coordinates to correctly predict the spherical aberration effects. The ball lenses can collect the laser light with great efficiency at a fraction of the cost for convectional GRIN or aspheric lenses. Furthermore, the small size allows the whole optical part to fit within standard hermetic packages.
A ray-tracing technique based on the radiation transfer equation is used to describe the spontaneous emission gain in active media. Using this approach analytical solutions for the intensity distribution and coherence function in the output plane of an active medium with parabolic transverse profiles of dielectric constant and gain coefficient are presented. Applicability of the approximation when contribution into output emission is made by only spontaneous sources adjacent to the far face region of an active medium is analyzed. This approximation is seen not to be applicable for many real situations and it is necessary to take into account the sources in the whole active medium. The effect of dielectric constant fluctuations on output coherence is treated by using the phase approximation of Huygens-Kirchhoff method.
Two modeling approaches for analyzing micro-size ball lenses will be described. Due to the low divergence angle of the light coming out of a single mode fiber (SMF), a Gaussian Optics analysis, integrated with ray tracing, is needed to design the optical subsystems such as fiber collimators. On the other hand, due to the large divergence angle of the light coming out of the laser diode (LD), an exact solution of Maxwell's equation which can be obtained by spherical harmonic expansion, is needed in order to predict the coupling efficiency from a LD to a SMF accurately. These models were applied to the cases of forward coupling and back reflections with various arrangements of the optical elements. Excellent agreement was found between the predictions of these two models and the experimental results. These models are very important for assemblies using micro-machined micro-optical parts since they have little or no allowance for alignment adjustments.
Much progress has been made recently in characterizing the emission from neon- like Yttrium exploding foil x-ray lasers. Concomitant with that effort, we have carried out detailed modeling to enhance our understanding of the experiments and improve their design. Our modeling includes target hydrodynamics, calculation of gain, and both ray and wave optics propagation. We will describe our modeling of Yt x-ray lasers, including first simulations using a two transverse dimensional gain calculation. Our calculations indicate that the time-integrated signal is very sensitive to the time history of the gain, because of the rapid sweep of the beam in angle measured with respect to the plane of the foil.
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